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Basic concepts: Measures of relative standing - z-score, quartiles, percentiles, Introduction to normal distribution,

- 1.Using sample data, it is possible to find a Z-score relating to the claim (the test-statistic).

__Significance level__

__Confidence Level $(1-\alpha$)____Significance Level ($\alpha$)____Critical Value ($Z_{\alpha}$)__0.90

0.10

?

0.95

0.05

?

0.99

0.01

?

Left Tail Test:

.

Right Tail Test:

.

Two tailed Test:

.

- 2.
**Finding the Critical Value**

With a significance level of $\alpha =0.075$ what is the resulting critical value of:a)A right-tailed test?b)A left-tailed test?c)A two-tailed test? - 3.Find the critical value from the following confidence levels for a right-tailed test:a)90% confidenceb)95% confidencec)99% confidence
- 4.
**Rejecting or Failing to Reject the Null Hypothesis**

The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

$H_0$: $p \leq 0.5$

$H_1$: $p$ > $0.5$

Using a significance level of $0.10$ (which corresponds to a critical value of $Z_\alpha=1.28$), and a Z-score of $Z=1.40$ relating to our Null Hypothesis;

Can we reject the Null Hypothesis? - 5.The following Null Hypothesis and Alternative Hypothesis have been derived from a statement:

$H_0$: $\mu \geq 175 lbs$

$H_1$: $\mu$ < $175 lbs$

Using a 95% confidence level and a Z-score of Z=-1.50 relating to our Null Hypothesis;

Can we reject the Null Hypothesis? - 6.The following claim is made.

“70% of Canadians own a pet”.

Given that the test-statistic is Z=2.75, with a confidence level of 90% what can be said about the proportions of pet owners in Canada?

39.

Hypothesis Testing

39.1

Null hypothesis and alternative hypothesis

39.2

Proving claims

39.3

Confidence levels, significance levels and critical values

39.4

Test statistics

39.5

Traditional hypothesis testing

39.6

P-value hypothesis testing

39.7

Mean hypothesis testing with t-distribution

39.8

Type 1 and type 2 errors

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